UNIVERSITY  OF  CALIFORNIA  PUBLICATIONS 

COLLEGE  OF  AGRICULTURE 

AGRICULTURAL  EXPERIMENT  STATION 

BERKELEY,  CALIFORNIA 


A  WHITE  FIR  VOLUME  TABLE 


BY 

DONALD    BRUCE 


BULLETIN  No.  329 

August,  1921. 


UNIVERSITY  OF  CALIFORNIA   PRESS 
BERKELEY,  CALIFORNIA 


David  P.  Barrows,  President  of  the  University. 

EXPEKIMENT  STATION  STAFF 

HEADS   OF  DIVISIONS 

Thomas  Forsyth  Hunt,  Dean. 

Edward  J.  Wickson,  Horticulture  (Emeritus). 

,  Director  of  Resident  Instruction. 

C.  M.  Haring,  Veterinary  Science,  Director  of  Agricultural  Experiment  Station. 

B.  H.  Crocheron,  Director  of  Agricultural  Extension. 
Hubert  E.  Van  Norman,  Vice-Director;  Dairy  Management. 

James  T.  Barrett,  Acting  Director  of  Citrus  Experiment  Station;  Plant  Pathology. 
William  A.  Setchell,  Botany. 
Myer  E.  Jaffa,  Nutrition. 
Ralph  E.  Smith,  Plant  Pathology. 
John  W.  Gilmore,  Agronomy. 
Charles  F.  Shaw,  Soil  Technology. 

John  W.  Gregg,  Landscape  Gardening  and  Floriculture. 
Frederic  T.  Bioletti,  Viticulture  and  Fruit  Products. 
Warren  T.  Clarke,  Agricultural  Extension. 
John  S.  Burd,  Agricultural  Chemistry. 
Charles  B.  Lipman,  Soil  Chemistry  and  Bacteriology. 
Ernest  B.  Babcock,  Genetics. 
Gordon  H.  True,  Animal  Husbandry. 
Walter  Mulford,  Forestry. 
Fritz  W.  Woll,  Animal  Nutrition. 
W.  P.  Kelley,  Agricultural  Chemistry. 
H.  J.  Quayle,  Entomology. 
Elwood  Mead,  Rural  Institutions. 
H.  S.  Reed,  Plant  Physiology. 
L.  D.  Batchelor,  Orchard  Management. 
J.  C.  Whitten,  Pomology, 
f Frank  Adams,  Irrigation  Investigations. 

C.  L.  Roadhouse,  Dairy  Industry. 

F.  L.  Griffin,  Agricultural  Education. 
John  E.  Dougherty,  Poultry  Husbandry. 
W.  B.  Herms,  Entomology  and  Parasitology. 
L.  J.  Fletcher,  Agricultural  Engineering. 
Edwin  C.  Voorhies,  Assistant  to  the  Dean. 

Division  of  Forestry 

Walter  Mulfokd  Woodbridge  Metcalf 

Donald  Bruce  Emanuel  Fritz 


t  In  cooperation  with  office  of  Public  Roads  and  Rural  Engineering,  U.  S.  Department  of 
Agriculture. 


A  WHITE  FIR  VOLUME  TABLE 

By  DONALD  BRUCE 


White  Fir  (Abies  concolor)  is  of  increasing  commercial  importance. 
A  few  years  ago  this  tree  was  usually  left  standing  during  logging 
operations,  as  the  value  of  lumber  to  be  secured  therefrom  was  not 
sufficient  to  repay  the  cost  of  manufacture.  To-day  it  is  usually  logged, 
and  at  a  profit,  and  in  the  future,  as  timber  becomes  scarcer,  its  value 
will  increase  still  more.  It  is  therefore  both  natural  that  no  accurate 
volume  table  for  this  species  should  have  previously  been  prepared,  and 
important  that  one  should  be  made  available  for  future  use. 

By  means  of  the  three-part  table  herein  presented,  the  average 
volume  in  board  feet  of  trees  of  given  diameters  and  heights  may  be 
accurately  determined.  The  table  will  not,  however,  give  more  than 
approximately  the  volume  of  an  individual  tree.  As  every  woodsman 
knows,  trees  of  the  same  diameter  and  height  may  vary  widely  in 
volume.  Some  trees  will  therefore  be  larger  than  the  tabular  values 
indicate  and  others  smaller,  but  in  averages  of  many  trees  these  dis- 
crepancies tend  to  counteract  each  other  and  for  large  groups  of  trees 
disappear. 

It  is  worth  while  to  emphasize  this  point.  Many  woodsmen  have 
noted  that  an  ocular  estimate  of  an  individual  tree  may  be  more  exact 
than  one  made  by  means  of  a  volume  table,  and  have  hence  thought 
such  tables  useless.  It  must  be  remembered,  however,  that  the  exact 
volumes  of  single  trees  are  rarely  of  use,  for  what  the  timber  owner  or 
operator  is  interested  in  is  the  combined  or  total  volume  of  all  the 
trees  of  a  given  species  on  some  specified  area.  Volume  tables  based 
on  the  averages  of  hundreds  of  accurately  measured  trees,  will  give 
this  result  as  exactly  as  it  is  possible  to  obtain  it,  for  they  reduce  to  a 
minimum  the  factor  of  the  personal  judgment  of  the  estimator.  This 
is  true,  however,  only  where  the  table  is  properly  used,  and  the  follow- 
ing precautions  must  be  observed. 

The  right  table  must  be  selected.  It  has  been  found  impossible  to 
prepare  a  single  table  that  would  be  accurate  for  the  whole  state  of 
California,  since  growing  conditions  differ  widely,  and  differences  in 
the  form  or  shape  of  trees  of  similar  height  and  diameter  result.  It 
has  been  established,  however,  that  this  form  is  essentially  similar  on 
two  tracts,  even  if  quite  remote  from  one  another,  if  the  maximum 


42  UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 

average  height  to  which  the  trees  grow  at  maturity  is  approximately 
the  same.  To  determine  the  "site"  of  any  given  tract,  then,  the  aver- 
age height  of  the  tallest  tenth  of  the  merchantable  trees  should  be 
estimated.  If  this  be  over  93^  16-foot  logs,  Table  I  should  be  used; 
if  73^2  or  under,  Table  III,  and  for  intermediate  values,  Table  II. 

Heights  should  be  measured  (or  estimated  if  the  estimator  has 
sufficient  skill)  in  16-foot  logs,  to  the  point  in  the  top  where  the  tree  is 
8  inches  in  diameter  inside  the  bark.  If,  in  accordance  with  the  logging 
practice  of  any  region,  it  is  evident  that  this  represents  too  close  a 
utilization,  a  deduction  for  unused  tops  should  be  made  in  connection 
with  the  cull  factor. 

Diameters  should  be  measured  (or  estimated)  outside  the  bark  at 
43^  feet  from  the  ground,  measuring  (in  the  case  of  sidehill  timber) 
from  the  average  ground  level. 

A  deduction  should  be  made  for  cull.  The  table  is  based  on  trees 
measured  as  if  sound,  unbroken,  and  to  be  completely  utilized.  Per- 
centage reductions  must  therefore  be  made  for 

(a)  Rot,  if  present. 

(b)  Breakage,  if  inevitable  even  with  careful  handling. 

(c)  Unused  tops  (see  above). 

(d)  Unused  stumps  (if  the  logging  practice  of  the  region  cuts 
stumps  materially  higher  than  18  inches). 

This  cull  percentage  for  white  fir  commonly  ranges  from  15  to  35 
per  cent,  including  all  the  above  items;  of  these  only  the  first  two, 
however,  are  of  much  importance. 


Bulletin  329 


A  WHITE  FIR  VOLUME   TABLE 


43 


TABLE  I. 

Site  I  (Tallest  10%  Merchantable  Trees  of  Stand  9.6  Logs  or  Over) 
Height  —  Number  of  16-Ft.  Logs 


Diameter 
Breast- 
High 
Inches 

10 '... 

12 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

3 
4 
4 
4 
5 

5 

7 

8 

10 

11 

9 
11 
13 
16 
19 

VOLU 

12 
15 
19 
23 

28 

ME  

30 
37 

Boar 

48 

D  FE 

ET  IN 

Tens 

14 

16 

18 

20 

13 
15 
17 
19 

23 

28 
32 
38 
44 

34 

42 
49 
58 
67 

45 
56 
66 

78 
90 

57 
70 
82 
97 
113 

68 

83 

98 

117 

136 

97 
114 
136 
159 

156 

182 

22 

24 

26 

28 

30 

49 
56 
63 
69 

75 

85 

95 

106 

117 

101 
114 
128 
142 
157 

128 
144 
161 
179 
198 

154 
174 
194 
216 

238 

181 
204 

227 
253 
279 

207 
233 
260 
290 
320 

234 
263 
294 
327 
360 

292 
327 
364 
401 

32 

34 

36... 

38 

441 

40 

128 
139 
151 

172 

188 
204 
221 
239 

217 
237 

258 
279 
301 

262 
286 
311 
336 
364 

307 
335 
364 
394 
426 

352 
384 
418 
452 
489 

397 
432 
471 
509 
551 

442 
481 
524 
567 
613 

487 

42 

528 

44 

577 

46 

625 

48 

676 

50 

257 

324 
347 
367 

391 
418 
443 
469 

458 
489 
520 
549 

525 
561 
596 
630 
666 

592 
632 
672 
710 
751 

659 
703 
748 
791 
836 

726 

52 

774 

54 

824 

56 

871 

58 

921 

60 

702 

794 

885 

936 

Stump  height  1.5  feet. 

Trees  scaled  in  16-foot  logs  with  0.3  foot  trimming  allowance,  to  8  inches 
diameter  inside  bark  in  top,  by  Scribner  Decimal  C.  rule  * 

Basis,  841  tree  measurements  taken  by  U.  S.  Forest  Service,  and  27  by  U.  S. 
Bureau  of  Plant  Pathology  on  the  Stanislaus  National  Forest  and  in  the  Yosemite 
National  Park.  Table  prepared  from  taper  curves  by  frustum  form  factor  method. 
Aggregate  check  against  basic  trees  shows  error  of  -0.24%. 


♦This  rule  has  been  adopted  as  standard  by  the  TJ.  S.  Forest  Service.    Its  values  multiplied  by  10  are 
essentially  the  same  as  those  of  the  Spaulding  rule,  which  is  the  legal  rule  for  California. 


44 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


TABLE  II. 

Site  II  (Tallest  10%  Merchantable  Trees  of  Stand  from  7.6  to  9.5  Logs.) 
Height  —  Number  of  16-Ft.  Logs 


Diameter 

Breast- 
High 
Inches 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

VOLU 

ME  

Boar 

D  FE 

ET  IN 

Tens 

10 

4 

6 

12 

15 

12 

5 

8 

13 

18 

14 

5 

9 

15 

22 

16 

5 

11 

18 

25 

33 

18 

5 

12 

20 

30 

39 

20 

13 
15 

23 

28 

35 
42 

46 
55 

58 
69 

22 

24 

16 

31 

48 

64 

80 

96 

112 

128 

26 

18 

36 

55 

75 

93 

112 

130 

148 

28 

42 

63 

85 

107 

128 

150 

172 

30 

46 

70 

94 

120 

144 

169 

194 

32 

52 

58 

79 
88 

106 
118 
131 

134 
148 
165 

162 
179 
197 

189 
209 
234 

216 
239 
266 

269 
298 

34 

36 

38 

144 

181 

218 

256 

293 

330 

40 

158 

199 

240 

281 

323 

365 

42 

218 
237 

263 

286 

308 
335 

353 
385 

397 
433 

482 

44 

46 

310 

338 

364 
396 

418 
454 

470 
512 

524 
569 

48 

50. 

366 
394 

428 
461 
493 
526 
561 

491 

528 
566 
603 
644 

554 
595 
638 
679 
726 

616 
662 
710 

756 

808 

52.... 

54... 

56... 

58.... 

60 

599 

687 

775 

864 

Stump  height  1.5  feet. 

Trees  scaled  in  16-foot  logs  with  0.3  foot  trimming  allowance,  to  8  inches 
diameter  inside  bark  in  top,  by  Scribner  Decimal  C.  rule. 

Basis:  124  tree  measurements  taken  by  U.  S.  Forest  Service  on  the  Plumas 
and  Tahoe  National  Forests,  and  179  by  the  U.  S.  Bureau  of  Plant  Pathology  on  the 
Sierra  National  Forest. 

Table  prepared  from  taper  curves  by  frustum  form  factor  method. 

Aggregate  check  against  basic  trees  shows  error  of  -0.42%. 


Bulletin  329 


A  WHITE   FIR  VOLUME   TABLE 


45 


TABLE  III. 

Site  III  (Tallest  10%  of  Merchantable  Trees  of  Stand  7.5  Logs  or  Under) 
Height  —  Number  of  16-Ft.  Logs 


Diameter 
Breast- 
High 
Inches 

10 

12 

14 

16 

18 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

4 
5 
5 
5 
5 

7 

9 

10 

11 

11 

13 
15 
16 

18 
20 

23 

26 
29 

VOLU 

34 

38 

ME  

48 

Boar 

D  FE 

ET  IN 

Tens 

20 

22 

12 
14 
15 
17 

22 

26 

28 
33 
38 

32 

38 
44 
52 

58 

43 
52 
60 
69 

78 

55 
65 
74 

85 
98 

103 
118 

24 

26 

28 

30 

41 

47 
53 
57 

64 

72 
80 
89 
97 

86 

96 

107 

118 

129 

109 
121 
135 

148 
165 

131 
146 
163 
179 
197 

155 
172 
190 
211 

232 

177 

197 
217 
241 
266 

32 

34 

36 

38 

40 

105 

142 
156 
169 
183 
199 

179 
196 
213 
231 
250 

217 

236 

258 
279 
302 

254 
277 
301 
326 
354 

291 
318 
346 
375 
406 

42 

44 

46 

48 

50 

52 

270 
291 
310 
329 
351 

325 
349 
374 

397 
424 

382 
410 
438 
466 
498 

437 

471 
502 
534 
571 

492 
530 
567 
602 
642 

54 

56 

58 

60 

372 

448 

526 

604 

683 

Stump  height  1.5  feet. 

Trees  scaled  in  16-ft.  logs  with  0.3  foot  trimming  allowance,  to  8  inches 
diameter  inside  bark  in  top,  by  Scribner  Decimal  C.  rule. 

Basis:  206  tree  measurements  taken  by  U.  S.  Bureau  of  Plant  Pathology  in 
the  Tahoe  and  Siskiyou  regions. 

Table  prepared  from  taper  curves  by  frustum  form  factor  method. 

Aggregate  check  against  basic  trees  shows  error  of  -0.17%. 


